DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, December 11, 2002 Padelford C-36 3:45 pm

Contact projective structures

Daniel Fox (UW)

Consider a family of paths on a contact manifold having the property that given a point in the manifold and a contact direction at that point there is a unique path of the family passing through the given point and tangent to the given contact direction. If these paths are among the unparameterized geodesics of some affine connection they constitute a contact projective structure. These are curved geometries modeled on the projectivization of a symplectic vector space, viewed as a homogeneous space for the symplectic group. I will describe an explicit solution of the local equivalence problem for these structures. The most interesting feature is an invariant torsion the vanishing of which implies the existence of distinguished curves transverse to the contact structure.

For more information about this seminar, visit the DG/PDE Seminar Web page (from the Math Department home page, www.math.washington.edu, follow the link Seminars, Colloquia, and Conferences).

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